Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Zhu, Rongchan"'
This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\mathbb{R}^+\times \mathbb{T}^2$ within the framework of paracontrolled calculus \cite{GIP15}. The model is given by the equation: \begin{equa
Externí odkaz:
http://arxiv.org/abs/2402.19137
We investigate the Langevin dynamics of various lattice formulations of the Yang-Mills-Higgs model, where the Higgs component takes values in $\mathbb{R}^N$, $\mathbb{S}^{N-1}$ or a Lie group. We prove the exponential ergodicity of the dynamics on th
Externí odkaz:
http://arxiv.org/abs/2401.13299
Autor:
Lü, Lin, Zhu, Rongchan
We establish the existence of infinitely many global and stationary solutions in $C(\mathbb{R};C^{\vartheta})$ space for some $\vartheta>0$ to the three dimensional Euler equations driven by an additive noise. The result is based on a new stochastic
Externí odkaz:
http://arxiv.org/abs/2401.09894
We consider stochastic forced Navier--Stokes equations on $\mathbb{R}^{3}$ starting from zero initial condition. The noise is linear multiplicative and the equations are perturbed by an additional body force. Based on the ideas of Albritton, Bru\'e a
Externí odkaz:
http://arxiv.org/abs/2309.03668
We consider a family of singular surface quasi-geostrophic equations $$ \partial_{t}\theta+u\cdot\nabla\theta=-\nu (-\Delta)^{\gamma/2}\theta+(-\Delta)^{\alpha/2}\xi,\qquad u=\nabla^{\perp}(-\Delta)^{-1/2}\theta, $$ on $[0,\infty)\times\mathbb{T}^{2}
Externí odkaz:
http://arxiv.org/abs/2308.14358
In this paper, we continue the study of large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$-component $\Phi^4$ model, in two spatial dimensions, using stochastic quantization methods and Dyson--Schwinger equations. We identify t
Externí odkaz:
http://arxiv.org/abs/2306.05166
We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to total dissi
Externí odkaz:
http://arxiv.org/abs/2305.08090
We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an $L^p$-in-time version of the Kolmogorov 4/5 law for the behavior of the averaged third order longitudinal structure function along the vanis
Externí odkaz:
http://arxiv.org/abs/2304.14470
Autor:
Zhang, Rui, Meng, Qi, Zhu, Rongchan, Wang, Yue, Shi, Wenlei, Zhang, Shihua, Ma, Zhi-Ming, Liu, Tie-Yan
In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical algorithms,
Externí odkaz:
http://arxiv.org/abs/2302.05104
The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of singular kernel
Externí odkaz:
http://arxiv.org/abs/2209.14002